In order to understand details in the seismic wave field observed on regional and global scales on the Earth's surface accurate modeling of 3D wave propagation is necessary. While numerical techniques are now routinely applied to local seismic wave propagation, only recently has the possibility of simulating wave propagation on larger scales in spherical geometry been investigated. We apply a high-order staggered-grid finite-difference scheme to the elastic wave equations in spherical coordinates [phi, theta, r]. Using regular grid spacing in a single domain the physical space is limited to spherical sections which do not include the axis theta = 0. While the staggering of the space-dependent fields improves the overall accuracy of the scheme, some of the tensor elements have to be interpolated to the required grid locations. By comparing with quasi-analytical solutions for layered Earth models we demonstrate the accuracy of the algorithm. Finally, the technique is used to study the effects of a source located in a simplified slab structure. The 3D technique will allow us to study the wave field due to laterally heterogeneous structures, such as subduction zones, plumes or oceanic ridges. (C) 2002 Elsevier Science B.V. All rights reserved.